Bevel Glitch with Subdivision Surface (Modifiers)
The bevels are helping the boundary loops stay sharp while being subdivided but the flat areas still get displaced according to the subdivision algorithm. 

This becomes apparent if you set your sub-d to level 1
Go to object properties - display - wire - draw all edges

this should help you see how, when the first sub-d is created, the unfortunate topology folds over the supporting edges. 

I've got no sure way of fixing this other than reworking the problem topology. 
Though, you might have better luck with not using bevel at all and only using sub-d with creased edges. (Albeit I doubt it will be enough for this kind of case)

Anyhow GL maybe someone else will come back with one operator solution for this.